
INTEREST TRBLES 



M. L. EDMUHDS. 



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V 



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SALEM, OREGON : 

EM. WAITE, STEAM PRINTER AND BOOKBINDER. 

18 8 7. 






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ABRIDGED 



INTEREST TABLES. 



fjC. 



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BY 



Lf/L. EDMUHDS. 



^^ 




SALEM, OREGON : 

E. M. WAITE, STEAM PEINTER AND BOOKBINDER. 

1887. 



'^t'U<^t. 



^>1' 



Entered according to Act of Congress, in ibe year 188(', by 

MILTON L. EDMUNDS, 
In the Office of the Librarian of Congress, at Washington. 



INTRODUCTION, 



The importance of a method that can be 
readily applied in the calculation of in- 
terest, has led to the exercise of considerable 
ingenuity in order to discover the shortest 
and simplest rule in practice. The object 
of this work is to present a method for 
computing interest, not only brief, but one 
that will give correct interest ; this being a 
feature in Avhich most methods are deficient 
in consequence of reckoning time incor- 
lectly. It may be readily seen that an error 
irises in the use of all methods for cal- 
culating interest, whereby the month is 
reckoned at 30 days, and consequently the 
year at 360 days; hence the objection to 
the favorite 6 per cent, method, also to 
various other methods, whicli, by reckon- 
ing 360 days to the year, give, for fractional 
parts of a year, an amount of interest ex- 



4 INTRODrCTION. 

ceediiig the exact interest by the same i-atio 
that 365 days exceed 860 days. 

Exact interest, obtained by reckoning 
365 days to the year, is growing in favoi* 
with bankers and other bnsiness men, is 
the method of interest used by the United 
States Government and by foreign corres- 
pondents, is the method of interest becom- 
ing the most popular, and whicli ultimately 
is destined to be in universal use. 

In solving problems in simple interest, 
the primary object is to find the interest on 
a given ])rincipal for a given time and rate- 
That method Avhich is the most natural and 
simple in principle, is to find tlie interest 
for one year by multiplying the principal 
by the rate, and then multiplying this in- 
terest by the time in years. The objection 
to this method, heretofore, has been in the 
difficulty of multiplying by the time, which, 
given in months and days, has been con- 
sidered incapable of being reduced to con- 
venient fractional parts of a year. The 
method of interest presented in this work. 
bi/ having all fractional parts of a year ex- 



iNTKODVC'TiOX. O 

pressed decbiially. enables us to follow tlie 
natural process, while at the same time it 
^ives the vshortest method possible for cal- 
eulating exact interest — a desideratum 
hitherto unsupplied bi/ any treatise on the 
subjeet. 

There being oiyo days in a year, it is im- 
possible to divide the year into months 
each containing an equal number of entire 
days, and therefore impracticable to reckon 
time in months. This difficulty may be 
obviated by using methods whereby in- 
terest is calculated for the number of days. 
Indeed, the only correct methods are those 
by which interest, for periods of time less 
than one year, is calculated for the exact 
number of days : and the most i^ractical 
method is that which by the most natural 
process, with the least amount of labor, will 
give exact interest. 

The amount of table-work, not aggre- 
gating one-half page, all of which should 
be thoroughly committed to memory, forms 
a desirable feature of this method; namely, 
the ease and rapidity with which we are 



(> IXTKODl'C TION. 

enabled to eoini^ute time and to reduce days 
to decimal years. It may also be observed 
tliat it" sucli periods of time as are in fre- 
([uent use have their decimal years mem- 
orized, the comi)utation of interest for these 
periods becomes susceptible of easy and 
rapid calculation. 

The method is conveniently treated un- 
der three cases, viz: To find the time; to 
express the time decimally ; and to find the 
exact interest To this is appended a gen- 
eral rule, also a variety of pi^oblems illus- 
trating the process ot obtaining, and mul- 
tiplying by, the decimal years. 

Having j)rosecuted the work with, the 
view of facilitating the calculation of in- 
terest, the author now submits his method 
to the consideration of those whose avoca- 
tions demand a practical treatise on this 
important subject, and leaves whatever 
merit the method deserves to' the decision 
of those competent to judge. 

M. L. Edmunds. 



ABRIDGED INTEREST TABLES, 



TO FIND THE TIME. 



lu order to comj3iite time readily, the 

following table, which gives the number of 

days in the year previous to the first day of 

each month, should be committed to 

memory : 

January May 120 September... 248 

Februarv....31 June lol October 278 

March.. !^ 59 Julv 181 November ...804 

April .90 August . . .21 2 December. . . .884 

To find the difference of time between 
two dates, we first find the day of the year 
of each date by adding the day of the month 
of each date respectivehj to the numbers in the 
table co}Tesponding to the given months, and 
then subtract the day of the year of the former 
date from the day of the year of the latter date, 
to find the difference of time in days be- 
tween two dates in the same year; or,- sub- 
tract the day of the year of the former date 
from 365 and add the remainder to the day of 



8 ABRIlXxKD INTEREST TABLES. 

the year of the latter date^ if the dates are in 
consecutive years, and the time less than 
one year • or, determine the number of entire 
years^ and then reckon the exact number of 
days remaining^ by the foregoing y^ules^ if the 
time exceeds one year ; and add 1 to the 
number of days found by the table, in passing 
over February in leap year. 

Example 1.— Should you want to find the 
day of the year corresponding to March 10th, 
determine the number of days iu the year pre- 
vious to the first day of March, which is showu 
by the table to be 59, to wiiich add the day of 
the month, and you find March 10th to be the 
69th day of the year. 

Example 2. — To find the difference of time 
between February 12th, the 48rd day of the year, 
and July 20th, the 201st day of the year, take the 
difference between 201 aud 48, which is 158, the 
difference of time in days. 

Example 3. — The difference of time in days 
between November 15th, the 319th day of the 
year, and February lOth, the 41st day of the 
year following, is found by adding the difference 
between 365 and 319, which is 46, the number of 
days from November 15th to the close of the 
year, to 41, which gives 87 days. 



ABRIDGED INTEREST TABLES. )) 

TO EXPRESS THE TIME DECIMALLY. 

Since each day is l-365th of a year, there 
will be as many 365ths of a year in any 
given time as there are days, and the frac- 
tional part of a year thus represented may 
be reduced to a decimal year by annexing 
ciphers to the number of days and dividing by 
365 ; the quotient thus obtained will be the 
time expressed decimally. 

Example. — Eeduce 97 days to a decimal 
year. 

Solution. — 97 days equal 97-365ths of a year ; 
and 97.0 divided by 365 equals .265-^; hence 97 
days equal .265- of a year. 

To facilitate the i>rocess of reducing days 
to decimal years, commit to memory the fol- 
lowing table : 

365X1= 365 365X4=1460 365X7=2555 
365x2= 730 365x5=1825 365x8=2920 
365 X 3=1095 365 X 6=2190 365 X 9=3285 



10 ABRIDGED INTEREST TABLES. 



THE DECIMAL YEAR. 

Ill reducing days to decimal years, we an- 
nex ciphers to the nuinber of days and di- 
vide by 365. Tlie division will in ^uost cases 
result in decimals which do not terminate, but, 
when expanded sufficiently far, will result in a 
L-eries of figures called the Vepetend, which will 
constantly repeat in the same order. Such dec- 
imals are called circulating decimals, and those 
repetends in which the terms of the first half are 
respectively ecjual to 9 minus the corresponding 
terms of the second half, are called comple- 
mentary rex)etends. 

Let the reduction of 97.6-f-o6o be continued 
five decimal places, and we have 2, the finite or 
non-repeating part of the decimal, and 6575, the 
first half of the rej)etend. Subtracting the 
terms of the first half of the repetend respect- 
ively from 9 gives 3424, the terms of fhe last 

half, and we have the mixed circulate .265753424, 
whose repetend is complementary. It is f here- 
fore evident that in making such reduction, or 
in memorizing a decimal year, it is unnecessary 
to continue the reduction or the memorizing 
further than is required to determine the first 
half of the repetend, since any number of terms 
following may be determined from the first half 
of the repeating part. 

When the number of days is 73, or a mul- 
tiple of 73, the corresponding decimal year ter- 
minates with tenths. When the number of 
days is 5, or a multiple of 5, the corresponding 
decimal year results in a circulate whose rep- 
etend begins with the first term of the decimal. 
All other decimal vears are circulates whose 



ABRIDGED INTEREST TABLES. 11 

repeteiuls begin with the second term of the dec- 
imal. The repetend of any circulating decimal 
year is complementary and consists of eight 
terms, and may be indicated by placing a period 
over the first and the last figures. 

As the number of decimal places ordinarily 
required is from three to five, the above prin- 
ciples of circulates are employed to expedite the 
l)roccss of reduction only when interest is re- 
quired on extremely large amounts, or when 
(lecimals are to be memorized. 

TO FIND THE EXACT INTEREST. 

Multiplying the principal by the rate of 
interest gives the interest for one year, and 
this interest multiplied by the time in 
years gives the required interest. 

The process of multiplying by the time, 
when expressed decimally, is performed by 
multiplying the interest for one year by the 
number of entire years ^ and each decimal di- 
vision of the interest for one year by the corres- 
ponding decimal part of the given time^ and 
taking the sum of these products. 

This process enables us to contract each 
product to the required denomination, and 
to reject all products of a lower denomina- 
tion than required in the entire i)roduct. 



12 ABRIDGED INTEREST TABLES. 

Example. — Eequired the interest of 
$3987, for 2 years and 316 days (2.86575-f 
years), at 5 per cent. 

OPERATION. 

$3987=Prineipal. 
.()o=Rate. 



199.35=Interest for one year. 
57e568.2=Tinie expressed decimally. 



398.70=Interest for 2 years. 
159.48=Interest for 8 tenths of a year. 
11.96=Interest for 6 hundredths of a year. 
I.OO=Interest for 5 thousandths of a year. 
.14=Interest for 7 ten-thousandths of a year. 
l=Interest for 5 hundred-thousandths of a 
year. 



|571.29=Required interest. 

Solution. — Multiplying the principal, ^8987, 
by the rate, .05, gives $199.35 interest for one 
year ; and this interest divided by 10, 100, 1000, 
etc., which may be effected by moving the dec- 
imal point one, two, three, etc. places to the left, 
will give $19.93+, $1.99-|-, 80.19^, etc., which 
equal the interest for one-tenth of a year, one- 
hundredth of a year, one-thousandth of a year, 
etc. By writing the number of entire years — 2, 
and the terms of the decimal years, which are 
tenths of a year — 8, hundredths of a year — 6, 
thousandths of a year — 5, etc., respectively un- 
der the rioiit hand terms of the interest for one 



ABKIDGKI) INTEREST TABLES. 18 

year — 8199.85, one-tenth of a year — S19.98-f, one- 
hundredth of a year — S1.99-H, one thousandth of 
a year — 80.19+, etc., we have the terms of the 
decimal years written in an inverted order, at 
the left of years, each properly written under 
that division of the year's interest to be multi- 
[)lied b^^ it. We multiply the interest for one 
year, one-tenth of a year, one-hundredth of a 
year, one-thousandth of a year, etc., respectively 
hy the number of entire years, tenths of a year, 
hundredths of a year, thousandths of a year, 
etc., increasing each of these products by as 
many units as would have been carried to it 
from the product of the rejected terms, and one 
more when the second term tow^ards the right 
in the product of the rejected terms is 5 or more 
than 5 ; and place the right hand terms of these 
products in the same column. The sum of 
these products gives the required interest. 

Note 1. — The rejected terms are the denominations lower 
than cents in the interest, and decimal divisions of the in' 
terest for one year. 

Note 2.— The terms of the decimal years must be extended 
one place farther to the left than the terms of the number ex- 
pressing the interest for one year, in order to obtain the last 
product, which is equal only to the number of units that 
would have been carried from the product of the rejected 
terms. 



14 AIUUTXUa) IXTKKKST TABLES. 

(iEXEKAL RULE. 

1. Multiply the principal by the rate of in- 
terest, to find the interest for one year, 

2. Write the number of entire years, ivhen 
not exceeding 9, using a cipher if the time is 
less than one year, under that part of the in- 
terest for one year, generally cents, which is of 
the lowest denomination in the required interest. 
Annex ciphers to the number of days and di- 
vide by S65, and tvrite the quotient figures, 
ivhich will be tenths of a year, hundredths of a 
year, thousandths of a year, etc., in a reverse 
order at the left of years, extending the terms 
of the decimal years, when interminate, one 
place farther to the left than the terms of the 
wunber expressing the interest for one year. 
If the number of entire years exceeds 9, write 
the number of entire years and the decimal part 
as separate multipliers. 

3. Regard the interest for one year di- 
vided by 10, LOO, 1000, etc., which tvill give 
the interest for one-tenth of a year, one-hun- 
dredth of a year, one-thousandth of a year, 
etc. : multiply these interests respectively by the 



ABRIDGEL) INTEREST TABLES. 15 

number of entire years, tenths of a year, hun- 
dredths of a year, thousandths of a year^ ete, ^ 
inereaslng each product by as many units as 
would have been carried to it from the product 
of the rejected termSj and one more when the 
second figure towards the^ right in the product 
of the rejected terms is 5 or more than 5 ; and 
take the sum of these products for the required 
interest. 

Note 1. — In reducing days to decimal years, when solving 
problems, pluce the number of days at the right of years, with 
the divisur, 365, at the right of days. Determine whether the 
first quotient figure is tenths of a year or hundredths of a year 
by observing whether one or two ciphers must be annexed to 
the number of days in order to be divisible by 305, If more 
ciphers are required they need not necessarily be annexed to 
the number of days, as the work may be made more concise 
by anut-xing them to tue remainders only. The operation may 
be still farther abbreviated by nut writing the divisor 365, nor 
the products of 365 by the quotient figures, since the work can 
be carried on mentally as in short division. 

Note 2 — Common interest may be calculated by the same 
process as exact interest; but in reducing days to decimal 
years, divide by 360 instead of 365. In this reduction the dec- 
imal, when interminate, results in a circulate whose repetend, 
consisting of but one figure, is readily found by observing 
when a quotient figure will constantly repeat. 

Note 3. — The following variation of the general rule wiii 
frequently be found more convenient: Multiply the principal by 
the rate, and this j^roduct by the exact number of days, and divide 
the result by 360 or 365, accordingly as common or exact interest is 
required. 



IG 



ABRIDGED INTEREST TABLES. 



ILLUSTRATIVE EXAMPLES. 

1. Required the in- 2. Required the in- 
terest of §225, for 2 years terest of §256.75, for 98 
and 40 days, at 8 per days, at 5 per cent, 
cent. 

OPERATION. OPERATION. 

§225 §256.75 

.08 .05 



18.00 




5901.2 


40.0(865 




865 


36.00 

1.80 


8500 


.16 


8285 


1 




91 r^Ci 



12.8875 
7452.0 

2.57 

.64 

5 

1 



98.0 
2000 
1750 
2900 



$87.97 Ans. 



§8.27 Ans. 



8. Required the in- 4. Required the in- 
terest of §400, for 10 terest of 860.25, for 5 
years and 22 da^^s, at 12 years and 78 days, at 7 
per cent. per cent. 



OPERA 

$400 
.12 


TION. 

22.00 
1000 


OPERATION 
' §60.25 

.07 


48.00 

2060.0 

10 


4.2175 
2.5 


21.09 

.84 


2.88 

1 

480.00 


§21.98 Ans. 


$482.89 Ans. 





78.0 



LIBRARY OF CONGRESS ^ 

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